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2008 | 28 | 1 | 23-34
Tytuł artykułu

Competition hypergraphs of digraphs with certain properties II. Hamiltonicity

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
If D = (V,A) is a digraph, its competition hypergraph 𝓒𝓗 (D) has vertex set V and e ⊆ V is an edge of 𝓒𝓗 (D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that $e = N_D⁻(v) = {w ∈ V|(w,v) ∈ A}$. We give characterizations of 𝓒𝓗 (D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ-cycle factor. The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [4] and Guichard [6].
Słowa kluczowe
Wydawca
Rocznik
Tom
28
Numer
1
Strony
23-34
Opis fizyczny
Daty
wydano
2008
otrzymano
2005-01-14
poprawiono
2007-09-24
zaakceptowano
2007-12-31
Twórcy
  • Faculty of Mathematics and Computer Science, TU Bergakademie Freiberg, Prüferstraße 1, D-09596 Freiberg, Germany
  • Institute of Mathematics, University of Lübeck, Wallstraß e 40, D-23560 Lübeck, Germany
Bibliografia
  • [1] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications (Springer, London, 2001).
  • [2] J.E. Cohen, Interval graphs and food webs: a finding and a problem (Rand Corporation Document 17696-PR, Santa Monica, CA, 1968).
  • [3] R.D. Dutton and R.C. Brigham, A characterization of competition graphs, Discrete Appl. Math. 6 (1983) 315-317, doi: 10.1016/0166-218X(83)90085-9.
  • [4] K.F. Fraughnaugh, J.R. Lundgren, S.K. Merz, J.S. Maybee and N.J. Pullman, Competition graphs of strongly connected and hamiltonian digraphs, SIAM J. Discrete Math. 8 (1995) 179-185, doi: 10.1137/S0895480191197234.
  • [5] H.J. Greenberg, J.R. Lundgren and J.S. Maybee, Inverting graphs of rectangular matrices, Discrete Appl. Math. 8 (1984) 255-265, doi: 10.1016/0166-218X(84)90123-9.
  • [6] D.R. Guichard, Competition graphs of hamiltonian digraphs, SIAM J. Discrete Math. 11 (1998) 128-134, doi: 10.1137/S089548019629735X.
  • [7] P. Hall, On representation of subsets, J. London Math. Soc. 10 (1935) 26-30, doi: 10.1112/jlms/s1-10.37.26.
  • [8] S.R. Kim, The competition number and its variants, in: J. Gimbel, J.W. Kennedy and L.V. Quintas (eds.), Quo vadis, graph theory?, Ann. of Discrete Math. 55 (1993) 313-326.
  • [9] J.R. Lundgren, Food webs, competition graphs, competition-common enemy graphs and niche graphs, in: F. Roberts (ed.), Applications of combinatorics and graph theory to the biological and social sciences, IMA 17 (Springer, New York, 1989) 221-243.
  • [10] J.R. Lundgren and J.S. Maybee, A characterization of graphs of competition number m, Discrete Appl. Math. 6 (1983) 319-322, doi: 10.1016/0166-218X(83)90086-0.
  • [11] F.S. Roberts, Competition graphs and phylogeny graphs, in: L. Lovasz (ed.), Graph theory and combinatorial biology; Proc. Int. Colloqu. Balatonlelle (Hungary) 1996, Bolyai Soc. Math. Studies 7 (Budapest, 1999) 333-362.
  • [12] F.S. Roberts and J.E. Steif, A characterization of competition graphs of arbitrary digraphs, Discrete Appl. Math. 6 (1983) 323-326, doi: 10.1016/0166-218X(83)90087-2.
  • [13] M. Sonntag and H.-M. Teichert, Competition hypergraphs, Discrete Appl. Math. 143 (2004) 324-329, doi: 10.1016/j.dam.2004.02.010.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1389
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